{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IVF27UMPU6ADUGOO3NEJTNPPKZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d551bc7a613bf5fb98b7e6c8b5f9b55423adca80a2f85dbd047b7043e9cc5e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-24T05:18:44Z","title_canon_sha256":"47a3a98ba759ecd43c984405e54b923d9f6ab9692c050692ba3b1bf9b07bd561"},"schema_version":"1.0","source":{"id":"1011.5300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5300","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5300v1","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5300","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"IVF27UMPU6AD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IVF27UMPU6ADUGOO","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IVF27UMP","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:8a2bacda8b5cdfa1c6a9188da639a8962e72a85aa6653bae28f5fc274827fce8","target":"graph","created_at":"2026-05-18T03:31:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For an ergodic hyperbolic measure $\\omega$ of a $C^{1+{\\alpha}}$ diffeomorphism, there is an $\\omega$ full-measured set $\\tilde\\Lambda$ such that every nonempty, compact and connected subset $V$ of $\\mathbb{M}_{inv}(\\tilde\\Lambda)$ coincides with the accumulating set of time averages of Dirac measures supported at {\\it one orbit}, where $\\mathbb{M}_{inv}(\\tilde\\Lambda)$ denotes the space of invariant measures supported on $\\tilde\\Lambda$. Such state points corresponding to a fixed $V$ are dense in the support $supp(\\omega)$. Moreover, $\\mathbb{M}_{inv}(\\tilde\\Lambda)$ can be accumulated by tim","authors_text":"Chao Liang, Wenxiang Sun, Xueting Tian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-24T05:18:44Z","title":"Ergodic Properties of Invariant Measures for C^{1+\\alpha} nonuniformly hyperbolic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5300","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:86545ed0dd6244ea85e85ede6beb4212378a074a511723dc44b65fae58953174","target":"record","created_at":"2026-05-18T03:31:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d551bc7a613bf5fb98b7e6c8b5f9b55423adca80a2f85dbd047b7043e9cc5e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-24T05:18:44Z","title_canon_sha256":"47a3a98ba759ecd43c984405e54b923d9f6ab9692c050692ba3b1bf9b07bd561"},"schema_version":"1.0","source":{"id":"1011.5300","kind":"arxiv","version":1}},"canonical_sha256":"454bafd18fa7803a19cedb4899b5ef5679fb581701369adb3f5315f851d2ee39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"454bafd18fa7803a19cedb4899b5ef5679fb581701369adb3f5315f851d2ee39","first_computed_at":"2026-05-18T03:31:45.274850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:45.274850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYZ8djwcmprPCaleh7gtDjNSAaRzVaotkEo0gHzbUKRKjBPKG238VZa8wfzsGdvHmi3LcZkgjls+WpfO3VezDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:45.275605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86545ed0dd6244ea85e85ede6beb4212378a074a511723dc44b65fae58953174","sha256:8a2bacda8b5cdfa1c6a9188da639a8962e72a85aa6653bae28f5fc274827fce8"],"state_sha256":"ea7edf74a7da0678b2f83686a305af4e16f6dae9ed790fd2e558b68c0db5d270"}